Apple Developer Connection Student Program/ADC Tools Sampler CD Disk 3 1999.iso/Metrowerks CodeWarrior/Java Support/Java_Source/Java2/src/java/util/Arrays.java

Java Source | 1999-05-28 | 75.0 KB | 2,189 lines | [TEXT/CWIE]

/*
 * @(#)Arrays.java    1.26 98/09/30
 *
 * Copyright 1997, 1998 by Sun Microsystems, Inc.,
 * 901 San Antonio Road, Palo Alto, California, 94303, U.S.A.
 * All rights reserved.
 *
 * This software is the confidential and proprietary information
 * of Sun Microsystems, Inc. ("Confidential Information").  You
 * shall not disclose such Confidential Information and shall use
 * it only in accordance with the terms of the license agreement
 * you entered into with Sun.
 */

package java.util;

/**
 * This class contains various methods for manipulating arrays (such as
 * sorting and searching).  It also contains a static factory that allows
 * arrays to be viewed as lists.<p>
 *
 * The documentation for the sorting and searching methods contained in this
 * class includes briefs description of the <i>implementations</i>.  Such
 * descriptions should be regarded as <i>implementation notes</i>, rather than
 * parts of the <i>specification</i>.  Implementors should feel free to
 * substitute other algorithms, so long as the specification itself is adhered
 * to.  (For example, the algorithm used by <tt>sort(Object[])</tt> does not
 * have to be a mergesort, but it does have to be <i>stable</i>.)
 *
 * @author  Josh Bloch
 * @version 1.26 09/30/98
 * @see Comparable
 * @see Comparator
 * @since JDK1.2
 */

public class Arrays {
    // Suppresses default constructor, ensuring non-instantiability.
    private Arrays() {
    }

    // Sorting

    /**
     * Sorts the specified array of longs into ascending numerical order.
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted.
     */
    public static void sort(long[] a) {
    sort1(a, 0, a.length);
    }

    /**
     * Sorts the specified range of the specified array of longs into
     * ascending numerical order.  The sorting algorithm is a tuned quicksort,
     * adapted from Jon L. Bentley and M. Douglas McIlroy's "Engineering a
     * Sort Function", Software-Practice and Experience, Vol. 23(11)
     * P. 1249-1265 (November 1993).  This algorithm offers n*log(n)
     * performance on many data sets that cause other quicksorts to degrade to
     * quadratic performance.
     *
     * @param a the array to be sorted.
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted.
     * @param toIndex the index of the last element (exclusive) to be sorted.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *           <tt>toIndex > a.length</tt>
     */
    public static void sort(long[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
    sort1(a, fromIndex, toIndex-fromIndex);
    }

    /**
     * Sorts the specified array of ints into ascending numerical order.
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted.
     */
    public static void sort(int[] a) {
    sort1(a, 0, a.length);
    }

    /**
     * Sorts the specified range of the specified array of ints into
     * ascending numerical order.  The sorting algorithm is a tuned quicksort,
     * adapted from Jon L. Bentley and M. Douglas McIlroy's "Engineering a
     * Sort Function", Software-Practice and Experience, Vol. 23(11)
     * P. 1249-1265 (November 1993).  This algorithm offers n*log(n)
     * performance on many data sets that cause other quicksorts to degrade to
     * quadratic performance.
     *
     * @param a the array to be sorted.
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted.
     * @param toIndex the index of the last element (exclusive) to be sorted.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *           <tt>toIndex > a.length</tt>
     */
    public static void sort(int[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
    sort1(a, fromIndex, toIndex-fromIndex);
    }

    /**
     * Sorts the specified array of shorts into ascending numerical order.
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted.
     */
    public static void sort(short[] a) {
    sort1(a, 0, a.length);
    }

    /**
     * Sorts the specified range of the specified array of shorts into
     * ascending numerical order.  The sorting algorithm is a tuned quicksort,
     * adapted from Jon L. Bentley and M. Douglas McIlroy's "Engineering a
     * Sort Function", Software-Practice and Experience, Vol. 23(11)
     * P. 1249-1265 (November 1993).  This algorithm offers n*log(n)
     * performance on many data sets that cause other quicksorts to degrade to
     * quadratic performance.
     *
     * @param a the array to be sorted.
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted.
     * @param toIndex the index of the last element (exclusive) to be sorted.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *           <tt>toIndex > a.length</tt>
     */
    public static void sort(short[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
    sort1(a, fromIndex, toIndex-fromIndex);
    }

    /**
     * Sorts the specified array of chars into ascending numerical order.
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted.
     */
    public static void sort(char[] a) {
    sort1(a, 0, a.length);
    }

    /**
     * Sorts the specified range of the specified array of chars into
     * ascending numerical order.  The sorting algorithm is a tuned quicksort,
     * adapted from Jon L. Bentley and M. Douglas McIlroy's "Engineering a
     * Sort Function", Software-Practice and Experience, Vol. 23(11)
     * P. 1249-1265 (November 1993).  This algorithm offers n*log(n)
     * performance on many data sets that cause other quicksorts to degrade to
     * quadratic performance.
     *
     * @param a the array to be sorted.
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted.
     * @param toIndex the index of the last element (exclusive) to be sorted.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *           <tt>toIndex > a.length</tt>
     */
    public static void sort(char[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
    sort1(a, fromIndex, toIndex-fromIndex);
    }

    /**
     * Sorts the specified array of bytes into ascending numerical order.
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted.
     */
    public static void sort(byte[] a) {
    sort1(a, 0, a.length);
    }

    /**
     * Sorts the specified range of the specified array of bytes into
     * ascending numerical order.  The sorting algorithm is a tuned quicksort,
     * adapted from Jon L. Bentley and M. Douglas McIlroy's "Engineering a
     * Sort Function", Software-Practice and Experience, Vol. 23(11)
     * P. 1249-1265 (November 1993).  This algorithm offers n*log(n)
     * performance on many data sets that cause other quicksorts to degrade to
     * quadratic performance.
     *
     * @param a the array to be sorted.
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted.
     * @param toIndex the index of the last element (exclusive) to be sorted.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *           <tt>toIndex > a.length</tt>
     */
    public static void sort(byte[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
    sort1(a, fromIndex, toIndex-fromIndex);
    }

    /**
     * Sorts the specified array of doubles into ascending numerical order.
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted.
     */
    public static void sort(double[] a) {
    sort2(a, 0, a.length);
    }

    /**
     * Sorts the specified range of the specified array of doubles into
     * ascending numerical order.  The sorting algorithm is a tuned quicksort,
     * adapted from Jon L. Bentley and M. Douglas McIlroy's "Engineering a
     * Sort Function", Software-Practice and Experience, Vol. 23(11)
     * P. 1249-1265 (November 1993).  This algorithm offers n*log(n)
     * performance on many data sets that cause other quicksorts to degrade to
     * quadratic performance.
     *
     * @param a the array to be sorted.
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted.
     * @param toIndex the index of the last element (exclusive) to be sorted.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *           <tt>toIndex > a.length</tt>
     */
    public static void sort(double[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
    sort2(a, fromIndex, toIndex);
    }

    /**
     * Sorts the specified array of floats into ascending numerical order.
     * The sorting algorithm is a tuned quicksort, adapted from Jon
     * L. Bentley and M. Douglas McIlroy's "Engineering a Sort Function",
     * Software-Practice and Experience, Vol. 23(11) P. 1249-1265 (November
     * 1993).  This algorithm offers n*log(n) performance on many data sets
     * that cause other quicksorts to degrade to quadratic performance.
     *
     * @param a the array to be sorted.
     */
    public static void sort(float[] a) {
    sort2(a, 0, a.length);
    }

    /**
     * Sorts the specified range of the specified array of floats into
     * ascending numerical order.  The sorting algorithm is a tuned quicksort,
     * adapted from Jon L. Bentley and M. Douglas McIlroy's "Engineering a
     * Sort Function", Software-Practice and Experience, Vol. 23(11)
     * P. 1249-1265 (November 1993).  This algorithm offers n*log(n)
     * performance on many data sets that cause other quicksorts to degrade to
     * quadratic performance.
     *
     * @param a the array to be sorted.
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted.
     * @param toIndex the index of the last element (exclusive) to be sorted.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *           <tt>toIndex > a.length</tt>
     */
    public static void sort(float[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
    sort2(a, fromIndex, toIndex);
    }

    private static void sort2(double a[], int fromIndex, int toIndex) {
        final long NEG_ZERO_BITS = Double.doubleToLongBits(-0.0d);
        /*
         * The sort is done in three phases to avoid the expense of using
         * NaN and -0.0 aware comparisons during the main sort.
         */

        /*
         * Preprocessing phase:  Move any NaN's to end of array, count the
         * number of -0.0's, and turn them into 0.0's.
         */
        int numNegZeros = 0;
        int i = fromIndex, n = toIndex;
        while(i < n) {
            if (a[i] != a[i]) {
                a[i] = a[--n];
                a[n] = Double.NaN;
            } else {
                if (a[i]==0 && Double.doubleToLongBits(a[i])==NEG_ZERO_BITS) {
                    a[i] = 0.0d;
                    numNegZeros++;
                }
                i++;
            }
        }

        // Main sort phase: quicksort everything but the NaN's
    sort1(a, fromIndex, n-fromIndex);

        // Postprocessing phase: change 0.0's to -0.0's as required
        if (numNegZeros != 0) {
            int j = binarySearch(a, 0.0d, fromIndex, n-1); // posn of ANY zero
            do {
                j--;
            } while (j>=0 && a[j]==0.0d);

            // j is now one less than the index of the FIRST zero
            for (int k=0; k<numNegZeros; k++)
                a[++j] = -0.0d;
        }
    }


    private static void sort2(float a[], int fromIndex, int toIndex) {
        final int NEG_ZERO_BITS = Float.floatToIntBits(-0.0f);
        /*
         * The sort is done in three phases to avoid the expense of using
         * NaN and -0.0 aware comparisons during the main sort.
         */

        /*
         * Preprocessing phase:  Move any NaN's to end of array, count the
         * number of -0.0's, and turn them into 0.0's.
         */
        int numNegZeros = 0;
        int i = fromIndex, n = toIndex;
        while(i < n) {
            if (a[i] != a[i]) {
                a[i] = a[--n];
                a[n] = Float.NaN;
            } else {
                if (a[i]==0 && Float.floatToIntBits(a[i])==NEG_ZERO_BITS) {
                    a[i] = 0.0f;
                    numNegZeros++;
                }
                i++;
            }
        }

        // Main sort phase: quicksort everything but the NaN's
    sort1(a, fromIndex, n-fromIndex);

        // Postprocessing phase: change 0.0's to -0.0's as required
        if (numNegZeros != 0) {
            int j = binarySearch(a, 0.0f, fromIndex, n-1); // posn of ANY zero
            do {
                j--;
            } while (j>=0 && a[j]==0.0f);

            // j is now one less than the index of the FIRST zero
            for (int k=0; k<numNegZeros; k++)
                a[++j] = -0.0f;
        }
    }


    /*
     * The code for each of the seven primitive types is largely identical.
     * C'est la vie.
     */

    /**
     * Sorts the specified sub-array of longs into ascending order.
     */
    private static void sort1(long x[], int off, int len) {
    // Insertion sort on smallest arrays
    if (len < 7) {
        for (int i=off; i<len+off; i++)
        for (int j=i; j>off && x[j-1]>x[j]; j--)
            swap(x, j, j-1);
        return;
    }

    // Choose a partition element, v
    int m = off + len/2;       // Small arrays, middle element
    if (len > 7) {
        int l = off;
        int n = off + len - 1;
        if (len > 40) {        // Big arrays, pseudomedian of 9
        int s = len/8;
        l = med3(x, l,     l+s, l+2*s);
        m = med3(x, m-s,   m,   m+s);
        n = med3(x, n-2*s, n-s, n);
        }
        m = med3(x, l, m, n); // Mid-size, med of 3
    }
    long v = x[m];

    // Establish Invariant: v* (<v)* (>v)* v*
    int a = off, b = a, c = off + len - 1, d = c;
    while(true) {
        while (b <= c && x[b] <= v) {
        if (x[b] == v)
            swap(x, a++, b);
        b++;
        }
        while (c >= b && x[c] >= v) {
        if (x[c] == v)
            swap(x, c, d--);
        c--;
        }
        if (b > c)
        break;
        swap(x, b++, c--);
    }

    // Swap partition elements back to middle
    int s, n = off + len;
    s = Math.min(a-off, b-a  );  vecswap(x, off, b-s, s);
    s = Math.min(d-c,   n-d-1);  vecswap(x, b,   n-s, s);

    // Recursively sort non-partition-elements
    if ((s = b-a) > 1)
        sort1(x, off, s);
    if ((s = d-c) > 1)
        sort1(x, n-s, s);
    }

    /**
     * Swaps x[a] with x[b].
     */
    private static void swap(long x[], int a, int b) {
    long t = x[a];
    x[a] = x[b];
    x[b] = t;
    }

    /**
     * Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
     */
    private static void vecswap(long x[], int a, int b, int n) {
    for (int i=0; i<n; i++, a++, b++)
        swap(x, a, b);
    }

    /**
     * Returns the index of the median of the three indexed longs.
     */
    private static int med3(long x[], int a, int b, int c) {
    return (x[a] < x[b] ?
        (x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
        (x[b] > x[c] ? b : x[a] > x[c] ? c : a));
    }

    /**
     * Sorts the specified sub-array of integers into ascending order.
     */
    private static void sort1(int x[], int off, int len) {
    // Insertion sort on smallest arrays
    if (len < 7) {
        for (int i=off; i<len+off; i++)
        for (int j=i; j>off && x[j-1]>x[j]; j--)
            swap(x, j, j-1);
        return;
    }

    // Choose a partition element, v
    int m = off + len/2;       // Small arrays, middle element
    if (len > 7) {
        int l = off;
        int n = off + len - 1;
        if (len > 40) {        // Big arrays, pseudomedian of 9
        int s = len/8;
        l = med3(x, l,     l+s, l+2*s);
        m = med3(x, m-s,   m,   m+s);
        n = med3(x, n-2*s, n-s, n);
        }
        m = med3(x, l, m, n); // Mid-size, med of 3
    }
    int v = x[m];

    // Establish Invariant: v* (<v)* (>v)* v*
    int a = off, b = a, c = off + len - 1, d = c;
    while(true) {
        while (b <= c && x[b] <= v) {
        if (x[b] == v)
            swap(x, a++, b);
        b++;
        }
        while (c >= b && x[c] >= v) {
        if (x[c] == v)
            swap(x, c, d--);
        c--;
        }
        if (b > c)
        break;
        swap(x, b++, c--);
    }

    // Swap partition elements back to middle
    int s, n = off + len;
    s = Math.min(a-off, b-a  );  vecswap(x, off, b-s, s);
    s = Math.min(d-c,   n-d-1);  vecswap(x, b,   n-s, s);

    // Recursively sort non-partition-elements
    if ((s = b-a) > 1)
        sort1(x, off, s);
    if ((s = d-c) > 1)
        sort1(x, n-s, s);
    }

    /**
     * Swaps x[a] with x[b].
     */
    private static void swap(int x[], int a, int b) {
    int t = x[a];
    x[a] = x[b];
    x[b] = t;
    }

    /**
     * Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
     */
    private static void vecswap(int x[], int a, int b, int n) {
    for (int i=0; i<n; i++, a++, b++)
        swap(x, a, b);
    }

    /**
     * Returns the index of the median of the three indexed integers.
     */
    private static int med3(int x[], int a, int b, int c) {
    return (x[a] < x[b] ?
        (x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
        (x[b] > x[c] ? b : x[a] > x[c] ? c : a));
    }

    /**
     * Sorts the specified sub-array of shorts into ascending order.
     */
    private static void sort1(short x[], int off, int len) {
    // Insertion sort on smallest arrays
    if (len < 7) {
        for (int i=off; i<len+off; i++)
        for (int j=i; j>off && x[j-1]>x[j]; j--)
            swap(x, j, j-1);
        return;
    }

    // Choose a partition element, v
    int m = off + len/2;       // Small arrays, middle element
    if (len > 7) {
        int l = off;
        int n = off + len - 1;
        if (len > 40) {        // Big arrays, pseudomedian of 9
        int s = len/8;
        l = med3(x, l,     l+s, l+2*s);
        m = med3(x, m-s,   m,   m+s);
        n = med3(x, n-2*s, n-s, n);
        }
        m = med3(x, l, m, n); // Mid-size, med of 3
    }
    short v = x[m];

    // Establish Invariant: v* (<v)* (>v)* v*
    int a = off, b = a, c = off + len - 1, d = c;
    while(true) {
        while (b <= c && x[b] <= v) {
        if (x[b] == v)
            swap(x, a++, b);
        b++;
        }
        while (c >= b && x[c] >= v) {
        if (x[c] == v)
            swap(x, c, d--);
        c--;
        }
        if (b > c)
        break;
        swap(x, b++, c--);
    }

    // Swap partition elements back to middle
    int s, n = off + len;
    s = Math.min(a-off, b-a  );  vecswap(x, off, b-s, s);
    s = Math.min(d-c,   n-d-1);  vecswap(x, b,   n-s, s);

    // Recursively sort non-partition-elements
    if ((s = b-a) > 1)
        sort1(x, off, s);
    if ((s = d-c) > 1)
        sort1(x, n-s, s);
    }

    /**
     * Swaps x[a] with x[b].
     */
    private static void swap(short x[], int a, int b) {
    short t = x[a];
    x[a] = x[b];
    x[b] = t;
    }

    /**
     * Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
     */
    private static void vecswap(short x[], int a, int b, int n) {
    for (int i=0; i<n; i++, a++, b++)
        swap(x, a, b);
    }

    /**
     * Returns the index of the median of the three indexed shorts.
     */
    private static int med3(short x[], int a, int b, int c) {
    return (x[a] < x[b] ?
        (x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
        (x[b] > x[c] ? b : x[a] > x[c] ? c : a));
    }


    /**
     * Sorts the specified sub-array of chars into ascending order.
     */
    private static void sort1(char x[], int off, int len) {
    // Insertion sort on smallest arrays
    if (len < 7) {
        for (int i=off; i<len+off; i++)
        for (int j=i; j>off && x[j-1]>x[j]; j--)
            swap(x, j, j-1);
        return;
    }

    // Choose a partition element, v
    int m = off + len/2;       // Small arrays, middle element
    if (len > 7) {
        int l = off;
        int n = off + len - 1;
        if (len > 40) {        // Big arrays, pseudomedian of 9
        int s = len/8;
        l = med3(x, l,     l+s, l+2*s);
        m = med3(x, m-s,   m,   m+s);
        n = med3(x, n-2*s, n-s, n);
        }
        m = med3(x, l, m, n); // Mid-size, med of 3
    }
    char v = x[m];

    // Establish Invariant: v* (<v)* (>v)* v*
    int a = off, b = a, c = off + len - 1, d = c;
    while(true) {
        while (b <= c && x[b] <= v) {
        if (x[b] == v)
            swap(x, a++, b);
        b++;
        }
        while (c >= b && x[c] >= v) {
        if (x[c] == v)
            swap(x, c, d--);
        c--;
        }
        if (b > c)
        break;
        swap(x, b++, c--);
    }

    // Swap partition elements back to middle
    int s, n = off + len;
    s = Math.min(a-off, b-a  );  vecswap(x, off, b-s, s);
    s = Math.min(d-c,   n-d-1);  vecswap(x, b,   n-s, s);

    // Recursively sort non-partition-elements
    if ((s = b-a) > 1)
        sort1(x, off, s);
    if ((s = d-c) > 1)
        sort1(x, n-s, s);
    }

    /**
     * Swaps x[a] with x[b].
     */
    private static void swap(char x[], int a, int b) {
    char t = x[a];
    x[a] = x[b];
    x[b] = t;
    }

    /**
     * Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
     */
    private static void vecswap(char x[], int a, int b, int n) {
    for (int i=0; i<n; i++, a++, b++)
        swap(x, a, b);
    }

    /**
     * Returns the index of the median of the three indexed chars.
     */
    private static int med3(char x[], int a, int b, int c) {
    return (x[a] < x[b] ?
        (x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
        (x[b] > x[c] ? b : x[a] > x[c] ? c : a));
    }


    /**
     * Sorts the specified sub-array of bytes into ascending order.
     */
    private static void sort1(byte x[], int off, int len) {
    // Insertion sort on smallest arrays
    if (len < 7) {
        for (int i=off; i<len+off; i++)
        for (int j=i; j>off && x[j-1]>x[j]; j--)
            swap(x, j, j-1);
        return;
    }

    // Choose a partition element, v
    int m = off + len/2;       // Small arrays, middle element
    if (len > 7) {
        int l = off;
        int n = off + len - 1;
        if (len > 40) {        // Big arrays, pseudomedian of 9
        int s = len/8;
        l = med3(x, l,     l+s, l+2*s);
        m = med3(x, m-s,   m,   m+s);
        n = med3(x, n-2*s, n-s, n);
        }
        m = med3(x, l, m, n); // Mid-size, med of 3
    }
    byte v = x[m];

    // Establish Invariant: v* (<v)* (>v)* v*
    int a = off, b = a, c = off + len - 1, d = c;
    while(true) {
        while (b <= c && x[b] <= v) {
        if (x[b] == v)
            swap(x, a++, b);
        b++;
        }
        while (c >= b && x[c] >= v) {
        if (x[c] == v)
            swap(x, c, d--);
        c--;
        }
        if (b > c)
        break;
        swap(x, b++, c--);
    }

    // Swap partition elements back to middle
    int s, n = off + len;
    s = Math.min(a-off, b-a  );  vecswap(x, off, b-s, s);
    s = Math.min(d-c,   n-d-1);  vecswap(x, b,   n-s, s);

    // Recursively sort non-partition-elements
    if ((s = b-a) > 1)
        sort1(x, off, s);
    if ((s = d-c) > 1)
        sort1(x, n-s, s);
    }

    /**
     * Swaps x[a] with x[b].
     */
    private static void swap(byte x[], int a, int b) {
    byte t = x[a];
    x[a] = x[b];
    x[b] = t;
    }

    /**
     * Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
     */
    private static void vecswap(byte x[], int a, int b, int n) {
    for (int i=0; i<n; i++, a++, b++)
        swap(x, a, b);
    }

    /**
     * Returns the index of the median of the three indexed bytes.
     */
    private static int med3(byte x[], int a, int b, int c) {
    return (x[a] < x[b] ?
        (x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
        (x[b] > x[c] ? b : x[a] > x[c] ? c : a));
    }


    /**
     * Sorts the specified sub-array of doubles into ascending order.
     */
    private static void sort1(double x[], int off, int len) {
    // Insertion sort on smallest arrays
    if (len < 7) {
        for (int i=off; i<len+off; i++)
        for (int j=i; j>off && x[j-1]>x[j]; j--)
            swap(x, j, j-1);
        return;
    }

    // Choose a partition element, v
    int m = off + len/2;       // Small arrays, middle element
    if (len > 7) {
        int l = off;
        int n = off + len - 1;
        if (len > 40) {        // Big arrays, pseudomedian of 9
        int s = len/8;
        l = med3(x, l,     l+s, l+2*s);
        m = med3(x, m-s,   m,   m+s);
        n = med3(x, n-2*s, n-s, n);
        }
        m = med3(x, l, m, n); // Mid-size, med of 3
    }
    double v = x[m];

    // Establish Invariant: v* (<v)* (>v)* v*
    int a = off, b = a, c = off + len - 1, d = c;
    while(true) {
        while (b <= c && x[b] <= v) {
        if (x[b] == v)
            swap(x, a++, b);
        b++;
        }
        while (c >= b && x[c] >= v) {
        if (x[c] == v)
            swap(x, c, d--);
        c--;
        }
        if (b > c)
        break;
        swap(x, b++, c--);
    }

    // Swap partition elements back to middle
    int s, n = off + len;
    s = Math.min(a-off, b-a  );  vecswap(x, off, b-s, s);
    s = Math.min(d-c,   n-d-1);  vecswap(x, b,   n-s, s);

    // Recursively sort non-partition-elements
    if ((s = b-a) > 1)
        sort1(x, off, s);
    if ((s = d-c) > 1)
        sort1(x, n-s, s);
    }

    /**
     * Swaps x[a] with x[b].
     */
    private static void swap(double x[], int a, int b) {
    double t = x[a];
    x[a] = x[b];
    x[b] = t;
    }

    /**
     * Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
     */
    private static void vecswap(double x[], int a, int b, int n) {
    for (int i=0; i<n; i++, a++, b++)
        swap(x, a, b);
    }

    /**
     * Returns the index of the median of the three indexed doubles.
     */
    private static int med3(double x[], int a, int b, int c) {
    return (x[a] < x[b] ?
        (x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
        (x[b] > x[c] ? b : x[a] > x[c] ? c : a));
    }


    /**
     * Sorts the specified sub-array of floats into ascending order.
     */
    private static void sort1(float x[], int off, int len) {
    // Insertion sort on smallest arrays
    if (len < 7) {
        for (int i=off; i<len+off; i++)
        for (int j=i; j>off && x[j-1]>x[j]; j--)
            swap(x, j, j-1);
        return;
    }

    // Choose a partition element, v
    int m = off + len/2;       // Small arrays, middle element
    if (len > 7) {
        int l = off;
        int n = off + len - 1;
        if (len > 40) {        // Big arrays, pseudomedian of 9
        int s = len/8;
        l = med3(x, l,     l+s, l+2*s);
        m = med3(x, m-s,   m,   m+s);
        n = med3(x, n-2*s, n-s, n);
        }
        m = med3(x, l, m, n); // Mid-size, med of 3
    }
    float v = x[m];

    // Establish Invariant: v* (<v)* (>v)* v*
    int a = off, b = a, c = off + len - 1, d = c;
    while(true) {
        while (b <= c && x[b] <= v) {
        if (x[b] == v)
            swap(x, a++, b);
        b++;
        }
        while (c >= b && x[c] >= v) {
        if (x[c] == v)
            swap(x, c, d--);
        c--;
        }
        if (b > c)
        break;
        swap(x, b++, c--);
    }

    // Swap partition elements back to middle
    int s, n = off + len;
    s = Math.min(a-off, b-a  );  vecswap(x, off, b-s, s);
    s = Math.min(d-c,   n-d-1);  vecswap(x, b,   n-s, s);

    // Recursively sort non-partition-elements
    if ((s = b-a) > 1)
        sort1(x, off, s);
    if ((s = d-c) > 1)
        sort1(x, n-s, s);
    }

    /**
     * Swaps x[a] with x[b].
     */
    private static void swap(float x[], int a, int b) {
    float t = x[a];
    x[a] = x[b];
    x[b] = t;
    }

    /**
     * Swaps x[a .. (a+n-1)] with x[b .. (b+n-1)].
     */
    private static void vecswap(float x[], int a, int b, int n) {
    for (int i=0; i<n; i++, a++, b++)
        swap(x, a, b);
    }

    /**
     * Returns the index of the median of the three indexed floats.
     */
    private static int med3(float x[], int a, int b, int c) {
    return (x[a] < x[b] ?
        (x[b] < x[c] ? b : x[a] < x[c] ? c : a) :
        (x[b] > x[c] ? b : x[a] > x[c] ? c : a));
    }


    /**
     * Sorts the specified array of objects into ascending order, according to
     * the <i>natural ordering</i> of its elements.  All elements in the array
     * must implement the <tt>Comparable</tt> interface.  Furthermore, all
     * elements in the array must be <i>mutually comparable</i> (that is,
     * <tt>e1.compareTo(e2)</tt> must not throw a <tt>ClassCastException</tt>
     * for any elements <tt>e1</tt> and <tt>e2</tt> in the array).<p>
     *
     * This sort is guaranteed to be <i>stable</i>:  equal elements will
     * not be reordered as a result of the sort.<p>
     *
     * The sorting algorithm is a modified mergesort (in which the merge is
     * omitted if the highest element in the low sublist is less than the
     * lowest element in the high sublist).  This algorithm offers guaranteed
     * n*log(n) performance, and can approach linear performance on nearly
     * sorted lists.
     *
     * @param a the array to be sorted.
     * @throws  ClassCastException if the array contains elements that are not
     *        <i>mutually comparable</i> (for example, strings and integers).
     * @see Comparable
     */
    public static void sort(Object[] a) {
        Object aux[] = (Object[])a.clone();
        mergeSort(aux, a, 0, a.length);
    }

    /**
     * Sorts the specified range of the specified array of objects into
     * ascending order, according to the <i>natural ordering</i> of its
     * elements.  All elements in this range must implement the
     * <tt>Comparable</tt> interface.  Furthermore, all elements in this range
     * must be <i>mutually comparable</i> (that is, <tt>e1.compareTo(e2)</tt>
     * must not throw a <tt>ClassCastException</tt> for any elements
     * <tt>e1</tt> and <tt>e2</tt> in the array).<p>
     *
     * This sort is guaranteed to be <i>stable</i>:  equal elements will
     * not be reordered as a result of the sort.<p>
     *
     * The sorting algorithm is a modified mergesort (in which the merge is
     * omitted if the highest element in the low sublist is less than the
     * lowest element in the high sublist).  This algorithm offers guaranteed
     * n*log(n) performance, and can approach linear performance on nearly
     * sorted lists.
     *
     * @param a the array to be sorted.
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted.
     * @param toIndex the index of the last element (exclusive) to be sorted.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *           <tt>toIndex > a.length</tt>
     * @throws    ClassCastException if the array contains elements that are
     *          not <i>mutually comparable</i> (for example, strings and
     *          integers).
     * @see Comparable
     */
    public static void sort(Object[] a, int fromIndex, int toIndex) {
        rangeCheck(a.length, fromIndex, toIndex);
        Object aux[] = (Object[])a.clone();  // Optimization opportunity
        mergeSort(aux, a, fromIndex, toIndex);
    }

    private static void mergeSort(Object src[], Object dest[],
                                  int low, int high) {
    int length = high - low;

    // Insertion sort on smallest arrays
    if (length < 7) {
        for (int i=low; i<high; i++)
        for (int j=i; j>low &&
                 ((Comparable)dest[j-1]).compareTo((Comparable)dest[j])>0; j--)
            swap(dest, j, j-1);
        return;
    }

        // Recursively sort halves of dest into src
        int mid = (low + high)/2;
        mergeSort(dest, src, low, mid);
        mergeSort(dest, src, mid, high);

        // If list is already sorted, just copy from src to dest.  This is an
        // optimization that results in faster sorts for nearly ordered lists.
        if (((Comparable)src[mid-1]).compareTo((Comparable)src[mid]) <= 0) {
           System.arraycopy(src, low, dest, low, length);
           return;
        }

        // Merge sorted halves (now in src) into dest
        for(int i = low, p = low, q = mid; i < high; i++) {
            if (q>=high || p<mid && ((Comparable)src[p]).compareTo(src[q])<=0)
                dest[i] = src[p++];
            else
                dest[i] = src[q++];
        }
    }

    /**
     * Swaps x[a] with x[b].
     */
    private static void swap(Object x[], int a, int b) {
    Object t = x[a];
    x[a] = x[b];
    x[b] = t;
    }

    /**
     * Sorts the specified array of objects according to the order induced by
     * the specified comparator.  All elements in the array must be
     * <i>mutually comparable</i> by the specified comparator (that is,
     * <tt>c.compare(e1, e2)</tt> must not throw a <tt>ClassCastException</tt>
     * for any elements <tt>e1</tt> and <tt>e2</tt> in the array).<p>
     *
     * This sort is guaranteed to be <i>stable</i>:  equal elements will
     * not be reordered as a result of the sort.<p>
     *
     * The sorting algorithm is a modified mergesort (in which the merge is
     * omitted if the highest element in the low sublist is less than the
     * lowest element in the high sublist).  This algorithm offers guaranteed
     * n*log(n) performance, and can approach linear performance on nearly
     * sorted lists.
     *
     * @param a the array to be sorted.
     * @param c the comparator to determine the order of the array.
     * @throws  ClassCastException if the array contains elements that are
     *        not <i>mutually comparable</i> using the specified comparator.
     * @see Comparator
     */
    public static void sort(Object[] a, Comparator c) {
        Object aux[] = (Object[])a.clone();
        mergeSort(aux, a, 0, a.length, c);
    }

    /**
     * Sorts the specified range of the specified array of objects according
     * to the order induced by the specified comparator.  All elements in the
     * range must be <i>mutually comparable</i> by the specified comparator
     * (that is, <tt>c.compare(e1, e2)</tt> must not throw a
     * <tt>ClassCastException</tt> for any elements <tt>e1</tt> and
     * <tt>e2</tt> in the range).<p>
     *
     * This sort is guaranteed to be <i>stable</i>:  equal elements will
     * not be reordered as a result of the sort.<p>
     *
     * The sorting algorithm is a modified mergesort (in which the merge is
     * omitted if the highest element in the low sublist is less than the
     * lowest element in the high sublist).  This algorithm offers guaranteed
     * n*log(n) performance, and can approach linear performance on nearly
     * sorted lists.
     *
     * @param a the array to be sorted.
     * @param fromIndex the index of the first element (inclusive) to be
     *        sorted.
     * @param toIndex the index of the last element (exclusive) to be sorted.
     * @param c the comparator to determine the order of the array.
     * @throws ClassCastException if the array contains elements that are not
     *           <i>mutually comparable</i> using the specified comparator.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *           <tt>toIndex > a.length</tt>
     * @see Comparator
     */
    public static void sort(Object[] a, int fromIndex, int toIndex,
                            Comparator c) {
        rangeCheck(a.length, fromIndex, toIndex);
        Object aux[] = (Object[])a.clone();
        mergeSort(aux, a, fromIndex, toIndex, c);
    }

    private static void mergeSort(Object src[], Object dest[],
                                  int low, int high, Comparator c) {
    int length = high - low;

    // Insertion sort on smallest arrays
    if (length < 7) {
        for (int i=low; i<high; i++)
        for (int j=i; j>low && c.compare(dest[j-1], dest[j])>0; j--)
            swap(dest, j, j-1);
        return;
    }

        // Recursively sort halves of dest into src
        int mid = (low + high)/2;
        mergeSort(dest, src, low, mid, c);
        mergeSort(dest, src, mid, high, c);

        // If list is already sorted, just copy from src to dest.  This is an
        // optimization that results in faster sorts for nearly ordered lists.
        if (c.compare(src[mid-1], src[mid]) <= 0) {
           System.arraycopy(src, low, dest, low, length);
           return;
        }

        // Merge sorted halves (now in src) into dest
        for(int i = low, p = low, q = mid; i < high; i++) {
            if (q>=high || p<mid && c.compare(src[p], src[q]) <= 0)
                dest[i] = src[p++];
            else
                dest[i] = src[q++];
        }
    }

    /**
     * Check that fromIndex and toIndex are in range, and throw an
     * appropriate exception if they aren't.
     */
    private static void rangeCheck(int arrayLen, int fromIndex, int toIndex) {
        if (fromIndex > toIndex)
            throw new IllegalArgumentException("fromIndex(" + fromIndex +
                       ") > toIndex(" + toIndex+")");
        if (fromIndex < 0)
            throw new ArrayIndexOutOfBoundsException(fromIndex);
        if (toIndex > arrayLen)
            throw new ArrayIndexOutOfBoundsException(toIndex);
    }

    // Searching

    /**
     * Searches the specified array of longs for the specified value using the
     * binary search algorithm.  The array <strong>must</strong> be sorted (as
     * by the <tt>sort</tt> method, above) prior to making this call.  If it
     * is not sorted, the results are undefined.  If the array contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.
     *
     * @param a the array to be searched.
     * @param key the value to be searched for.
     * @return index of the search key, if it is contained in the list;
     *           otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *           <i>insertion point</i> is defined as the point at which the
     *           key would be inserted into the list: the index of the first
     *           element greater than the key, or <tt>list.size()</tt>, if all
     *           elements in the list are less than the specified key.  Note
     *           that this guarantees that the return value will be >= 0 if
     *           and only if the key is found.
     * @see #sort(long[])
     */
    public static int binarySearch(long[] a, long key) {
    int low = 0;
    int high = a.length-1;

    while (low <= high) {
        int mid =(low + high)/2;
        long midVal = a[mid];

        if (midVal < key)
        low = mid + 1;
        else if (midVal > key)
        high = mid - 1;
        else
        return mid; // key found
    }
    return -(low + 1);  // key not found.
    }


    /**
     * Searches the specified array of ints for the specified value using the
     * binary search algorithm.  The array <strong>must</strong> be sorted (as
     * by the <tt>sort</tt> method, above) prior to making this call.  If it
     * is not sorted, the results are undefined.  If the array contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.
     *
     * @param a the array to be searched.
     * @param key the value to be searched for.
     * @return index of the search key, if it is contained in the list;
     *           otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *           <i>insertion point</i> is defined as the point at which the
     *           key would be inserted into the list: the index of the first
     *           element greater than the key, or <tt>list.size()</tt>, if all
     *           elements in the list are less than the specified key.  Note
     *           that this guarantees that the return value will be >= 0 if
     *           and only if the key is found.
     * @see #sort(int[])
     */
    public static int binarySearch(int[] a, int key) {
    int low = 0;
    int high = a.length-1;

    while (low <= high) {
        int mid =(low + high)/2;
        int midVal = a[mid];

        if (midVal < key)
        low = mid + 1;
        else if (midVal > key)
        high = mid - 1;
        else
        return mid; // key found
    }
    return -(low + 1);  // key not found.
    }

    /**
     * Searches the specified array of shorts for the specified value using
     * the binary search algorithm.  The array <strong>must</strong> be sorted
     * (as by the <tt>sort</tt> method, above) prior to making this call.  If
     * it is not sorted, the results are undefined.  If the array contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.
     *
     * @param a the array to be searched.
     * @param key the value to be searched for.
     * @return index of the search key, if it is contained in the list;
     *           otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *           <i>insertion point</i> is defined as the point at which the
     *           key would be inserted into the list: the index of the first
     *           element greater than the key, or <tt>list.size()</tt>, if all
     *           elements in the list are less than the specified key.  Note
     *           that this guarantees that the return value will be >= 0 if
     *           and only if the key is found.
     * @see #sort(short[])
     */
    public static int binarySearch(short[] a, short key) {
    int low = 0;
    int high = a.length-1;

    while (low <= high) {
        int mid =(low + high)/2;
        short midVal = a[mid];

        if (midVal < key)
        low = mid + 1;
        else if (midVal > key)
        high = mid - 1;
        else
        return mid; // key found
    }
    return -(low + 1);  // key not found.
    }

    /**
     * Searches the specified array of chars for the specified value using the
     * binary search algorithm.  The array <strong>must</strong> be sorted (as
     * by the <tt>sort</tt> method, above) prior to making this call.  If it
     * is not sorted, the results are undefined.  If the array contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.
     *
     * @param a the array to be searched.
     * @param key the value to be searched for.
     * @return index of the search key, if it is contained in the list;
     *           otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *           <i>insertion point</i> is defined as the point at which the
     *           key would be inserted into the list: the index of the first
     *           element greater than the key, or <tt>list.size()</tt>, if all
     *           elements in the list are less than the specified key.  Note
     *           that this guarantees that the return value will be >= 0 if
     *           and only if the key is found.
     * @see #sort(char[])
     */
    public static int binarySearch(char[] a, char key) {
    int low = 0;
    int high = a.length-1;

    while (low <= high) {
        int mid =(low + high)/2;
        char midVal = a[mid];

        if (midVal < key)
        low = mid + 1;
        else if (midVal > key)
        high = mid - 1;
        else
        return mid; // key found
    }
    return -(low + 1);  // key not found.
    }

    /**
     * Searches the specified array of bytes for the specified value using the
     * binary search algorithm.  The array <strong>must</strong> be sorted (as
     * by the <tt>sort</tt> method, above) prior to making this call.  If it
     * is not sorted, the results are undefined.  If the array contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.
     *
     * @param a the array to be searched.
     * @param key the value to be searched for.
     * @return index of the search key, if it is contained in the list;
     *           otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *           <i>insertion point</i> is defined as the point at which the
     *           key would be inserted into the list: the index of the first
     *           element greater than the key, or <tt>list.size()</tt>, if all
     *           elements in the list are less than the specified key.  Note
     *           that this guarantees that the return value will be >= 0 if
     *           and only if the key is found.
     * @see #sort(byte[])
     */
    public static int binarySearch(byte[] a, byte key) {
    int low = 0;
    int high = a.length-1;

    while (low <= high) {
        int mid =(low + high)/2;
        byte midVal = a[mid];

        if (midVal < key)
        low = mid + 1;
        else if (midVal > key)
        high = mid - 1;
        else
        return mid; // key found
    }
    return -(low + 1);  // key not found.
    }

    /**
     * Searches the specified array of doubles for the specified value using
     * the binary search algorithm.  The array <strong>must</strong> be sorted
     * (as by the <tt>sort</tt> method, above) prior to making this call.  If
     * it is not sorted, the results are undefined.  If the array contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.
     *
     * @param a the array to be searched.
     * @param key the value to be searched for.
     * @return index of the search key, if it is contained in the list;
     *           otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *           <i>insertion point</i> is defined as the point at which the
     *           key would be inserted into the list: the index of the first
     *           element greater than the key, or <tt>list.size()</tt>, if all
     *           elements in the list are less than the specified key.  Note
     *           that this guarantees that the return value will be >= 0 if
     *           and only if the key is found.
     * @see #sort(double[])
     */
    public static int binarySearch(double[] a, double key) {
        return binarySearch(a, key, 0, a.length-1);
    }

    private static int binarySearch(double[] a, double key, int low,int high) {
    while (low <= high) {
        int mid =(low + high)/2;
        double midVal = a[mid];

            int cmp;
            if (midVal < key) {
                cmp = -1;   // Neither val is NaN, thisVal is smaller
            } else if (midVal > key) {
                cmp = 1;    // Neither val is NaN, thisVal is larger
            } else {
                long midBits = Double.doubleToLongBits(midVal);
                long keyBits = Double.doubleToLongBits(key);
                cmp = (midBits == keyBits ?  0 : // Values are equal
                       (midBits < keyBits ? -1 : // (-0.0, 0.0) or (!NaN, NaN)
                        1));                     // (0.0, -0.0) or (NaN, !NaN)
            }

        if (cmp < 0)
        low = mid + 1;
        else if (cmp > 0)
        high = mid - 1;
        else
        return mid; // key found
    }
    return -(low + 1);  // key not found.
    }

    /**
     * Searches the specified array of floats for the specified value using
     * the binary search algorithm.  The array <strong>must</strong> be sorted
     * (as by the <tt>sort</tt> method, above) prior to making this call.  If
     * it is not sorted, the results are undefined.  If the array contains
     * multiple elements with the specified value, there is no guarantee which
     * one will be found.
     *
     * @param a the array to be searched.
     * @param key the value to be searched for.
     * @return index of the search key, if it is contained in the list;
     *           otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *           <i>insertion point</i> is defined as the point at which the
     *           key would be inserted into the list: the index of the first
     *           element greater than the key, or <tt>list.size()</tt>, if all
     *           elements in the list are less than the specified key.  Note
     *           that this guarantees that the return value will be >= 0 if
     *           and only if the key is found.
     * @see #sort(float[])
     */
    public static int binarySearch(float[] a, float key) {
        return binarySearch(a, key, 0, a.length-1);
    }

    private static int binarySearch(float[] a, float key, int low,int high) {
    while (low <= high) {
        int mid =(low + high)/2;
        float midVal = a[mid];

            int cmp;
            if (midVal < key) {
                cmp = -1;   // Neither val is NaN, thisVal is smaller
            } else if (midVal > key) {
                cmp = 1;    // Neither val is NaN, thisVal is larger
            } else {
                int midBits = Float.floatToIntBits(midVal);
                int keyBits = Float.floatToIntBits(key);
                cmp = (midBits == keyBits ?  0 : // Values are equal
                       (midBits < keyBits ? -1 : // (-0.0, 0.0) or (!NaN, NaN)
                        1));                     // (0.0, -0.0) or (NaN, !NaN)
            }

        if (cmp < 0)
        low = mid + 1;
        else if (cmp > 0)
        high = mid - 1;
        else
        return mid; // key found
    }
    return -(low + 1);  // key not found.
    }


    /**
     * Searches the specified array for the specified object using the binary
     * search algorithm.  The array must be sorted into ascending order
     * according to the <i>natural ordering</i> of its elements (as by
     * <tt>Sort(Object[]</tt>), above) prior to making this call.  If it is
     * not sorted, the results are undefined.  If the array contains multiple
     * elements equal to the specified object, there is no guarantee which
     * one will be found.
     *
     * @param a the array to be searched.
     * @param key the value to be searched for.
     * @return index of the search key, if it is contained in the list;
     *           otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *           <i>insertion point</i> is defined as the point at which the
     *           key would be inserted into the list: the index of the first
     *           element greater than the key, or <tt>list.size()</tt>, if all
     *           elements in the list are less than the specified key.  Note
     *           that this guarantees that the return value will be >= 0 if
     *           and only if the key is found.
     * @throws ClassCastException if the array contains elements that are not
     *           <i>mutually comparable</i> (for example, strings and integers),
     *         or the search key in not mutually comparable with the elements
     *         of the array.
     * @see Comparable
     * @see #sort(Object[])
     */
    public static int binarySearch(Object[] a, Object key) {
    int low = 0;
    int high = a.length-1;

    while (low <= high) {
        int mid =(low + high)/2;
        Object midVal = a[mid];
        int cmp = ((Comparable)midVal).compareTo(key);

        if (cmp < 0)
        low = mid + 1;
        else if (cmp > 0)
        high = mid - 1;
        else
        return mid; // key found
    }
    return -(low + 1);  // key not found.
    }

    /**
     * Searches the specified array for the specified object using the binary
     * search algorithm.  The array must be sorted into ascending order
     * according to the specified comparator (as by the <tt>Sort(Object[],
     * Comparator)</tt> method, above), prior to making this call.  If it is
     * not sorted, the results are undefined.  If the array contains multiple
     * elements equal to the specified object, there is no guarantee which one
     * will be found.
     *
     * @param a the array to be searched.
     * @param key the value to be searched for.
     * @param c the comparator by which the array is ordered.
     * @return index of the search key, if it is contained in the list;
     *           otherwise, <tt>(-(<i>insertion point</i>) - 1)</tt>.  The
     *           <i>insertion point</i> is defined as the point at which the
     *           key would be inserted into the list: the index of the first
     *           element greater than the key, or <tt>list.size()</tt>, if all
     *           elements in the list are less than the specified key.  Note
     *           that this guarantees that the return value will be >= 0 if
     *           and only if the key is found.
     * @throws ClassCastException if the array contains elements that are not
     *           <i>mutually comparable</i> using the specified comparator,
     *           or the search key in not mutually comparable with the
     *           elements of the array using this comparator.
     * @see Comparable
     * @see #sort(Object[], Comparator)
     */
    public static int binarySearch(Object[] a, Object key, Comparator c) {
    int low = 0;
    int high = a.length-1;

    while (low <= high) {
        int mid =(low + high)/2;
        Object midVal = a[mid];
        int cmp = c.compare(midVal, key);

        if (cmp < 0)
        low = mid + 1;
        else if (cmp > 0)
        high = mid - 1;
        else
        return mid; // key found
    }
    return -(low + 1);  // key not found.
    }


    // Equality Testing

    /**
     * Returns <tt>true</tt> if the two specified arrays of longs are
     * <i>equal</i> to one another.  Two arrays are considered equal if both
     * arrays contain the same number of elements, and all corresponding pairs
     * of elements in the two arrays are equal.  In other words, two arrays
     * are equal if they contain the same elements in the same order.  Also,
     * two array references are considered equal if both are <tt>null</tt>.<p>
     *
     * @param a one array to be tested for equality.
     * @param a2 the other array to be tested for equality.
     * @return <tt>true</tt> if the two arrays are equal.
     */
    public static boolean equals(long[] a, long[] a2) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
            if (a[i] != a2[i])
                return false;

        return true;
    }

    /**
     * Returns <tt>true</tt> if the two specified arrays of ints are
     * <i>equal</i> to one another.  Two arrays are considered equal if both
     * arrays contain the same number of elements, and all corresponding pairs
     * of elements in the two arrays are equal.  In other words, two arrays
     * are equal if they contain the same elements in the same order.  Also,
     * two array references are considered equal if both are <tt>null</tt>.<p>
     *
     * @param a one array to be tested for equality.
     * @param a2 the other array to be tested for equality.
     * @return <tt>true</tt> if the two arrays are equal.
     */
    public static boolean equals(int[] a, int[] a2) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
            if (a[i] != a2[i])
                return false;

        return true;
    }

    /**
     * Returns <tt>true</tt> if the two specified arrays of shorts are
     * <i>equal</i> to one another.  Two arrays are considered equal if both
     * arrays contain the same number of elements, and all corresponding pairs
     * of elements in the two arrays are equal.  In other words, two arrays
     * are equal if they contain the same elements in the same order.  Also,
     * two array references are considered equal if both are <tt>null</tt>.<p>
     *
     * @param a one array to be tested for equality.
     * @param a2 the other array to be tested for equality.
     * @return <tt>true</tt> if the two arrays are equal.
     */
    public static boolean equals(short[] a, short a2[]) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
            if (a[i] != a2[i])
                return false;

        return true;
    }

    /**
     * Returns <tt>true</tt> if the two specified arrays of chars are
     * <i>equal</i> to one another.  Two arrays are considered equal if both
     * arrays contain the same number of elements, and all corresponding pairs
     * of elements in the two arrays are equal.  In other words, two arrays
     * are equal if they contain the same elements in the same order.  Also,
     * two array references are considered equal if both are <tt>null</tt>.<p>
     *
     * @param a one array to be tested for equality.
     * @param a2 the other array to be tested for equality.
     * @return <tt>true</tt> if the two arrays are equal.
     */
    public static boolean equals(char[] a, char[] a2) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
            if (a[i] != a2[i])
                return false;

        return true;
    }

    /**
     * Returns <tt>true</tt> if the two specified arrays of bytes are
     * <i>equal</i> to one another.  Two arrays are considered equal if both
     * arrays contain the same number of elements, and all corresponding pairs
     * of elements in the two arrays are equal.  In other words, two arrays
     * are equal if they contain the same elements in the same order.  Also,
     * two array references are considered equal if both are <tt>null</tt>.<p>
     *
     * @param a one array to be tested for equality.
     * @param a2 the other array to be tested for equality.
     * @return <tt>true</tt> if the two arrays are equal.
     */
    public static boolean equals(byte[] a, byte[] a2) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
            if (a[i] != a2[i])
                return false;

        return true;
    }

    /**
     * Returns <tt>true</tt> if the two specified arrays of equals are
     * <i>equal</i> to one another.  Two arrays are considered equal if both
     * arrays contain the same number of elements, and all corresponding pairs
     * of elements in the two arrays are equal.  In other words, two arrays
     * are equal if they contain the same elements in the same order.  Also,
     * two array references are considered equal if both are <tt>null</tt>.<p>
     *
     * @param a one array to be tested for equality.
     * @param a2 the other array to be tested for equality.
     * @return <tt>true</tt> if the two arrays are equal.
     */
    public static boolean equals(boolean[] a, boolean[] a2) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
            if (a[i] != a2[i])
                return false;

        return true;
    }

    /**
     * Returns <tt>true</tt> if the two specified arrays of doubles are
     * <i>equal</i> to one another.  Two arrays are considered equal if both
     * arrays contain the same number of elements, and all corresponding pairs
     * of elements in the two arrays are equal.  In other words, two arrays
     * are equal if they contain the same elements in the same order.  Also,
     * two array references are considered equal if both are <tt>null</tt>.<p>
     *
     * Two doubles <tt>d1</tt> and <tt>d2</tt> are considered equal if:
     * <pre>    <tt>new Double(d1).equals(new Double(d2))</tt></pre>
     * (Unlike the <tt>==</tt> operator, this method considers
     * <tt>NaN</tt> equals to itself, and 0.0d unequal to -0.0d.)
     *
     * @param a one array to be tested for equality.
     * @param a2 the other array to be tested for equality.
     * @return <tt>true</tt> if the two arrays are equal.
     * @see Double#equals(Double)
     */
    public static boolean equals(double[] a, double[] a2) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
        if (Double.doubleToLongBits(a[i])!=Double.doubleToLongBits(a2[i]))
                return false;

        return true;
    }

    /**
     * Returns <tt>true</tt> if the two specified arrays of floats are
     * <i>equal</i> to one another.  Two arrays are considered equal if both
     * arrays contain the same number of elements, and all corresponding pairs
     * of elements in the two arrays are equal.  In other words, two arrays
     * are equal if they contain the same elements in the same order.  Also,
     * two array references are considered equal if both are <tt>null</tt>.<p>
     *
     * Two doubles <tt>d1</tt> and <tt>d2</tt> are considered equal if:
     * <pre>    <tt>new Double(d1).equals(new Double(d2))</tt></pre>
     * (Unlike the <tt>==</tt> operator, this method considers
     * <tt>NaN</tt> equals to itself, and 0.0d unequal to -0.0d.)
     *
     * @param a one array to be tested for equality.
     * @param a2 the other array to be tested for equality.
     * @return <tt>true</tt> if the two arrays are equal.
     * @see Double#equals(Double)
     */
    public static boolean equals(float[] a, float[] a2) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++)
        if (Float.floatToIntBits(a[i])!=Float.floatToIntBits(a2[i]))
                return false;

        return true;
    }


    /**
     * Returns <tt>true</tt> if the two specified arrays of Objects are
     * <i>equal</i> to one another.  The two arrays are considered equal if
     * both arrays contain the same number of elements, and all corresponding
     * pairs of elements in the two arrays are equal.  Two objects <tt>e1</tt>
     * and <tt>e2</tt> are considered <i>equal</i> if <tt>(e1==null ? e2==null
     * : e1.equals(e2))</tt>.  In other words, the two arrays are equal if
     * they contain the same elements in the same order.  Also, two array
     * references are considered equal if both are <tt>null</tt>.<p>
     *
     * @param a one array to be tested for equality.
     * @param a2 the other array to be tested for equality.
     * @return <tt>true</tt> if the two arrays are equal.
     */
    public static boolean equals(Object[] a, Object[] a2) {
        if (a==a2)
            return true;
        if (a==null || a2==null)
            return false;

        int length = a.length;
        if (a2.length != length)
            return false;

        for (int i=0; i<length; i++) {
            Object o1 = a[i];
            Object o2 = a2[i];
            if (!(o1==null ? o2==null : o1.equals(o2)))
                return false;
        }

        return true;
    }


    // Filling

    /**
     * Assigns the specified long value to each element of the specified array
     * of longs.
     *
     * @param a the array to be filled.
     * @param val the value to be stored in all elements of the array.
     */
    public static void fill(long[] a, long val) {
        fill(a, 0, a.length, val);
    }

    /**
     * Assigns the specified long value to each element of the specified
     * range of the specified array of longs.
     *
     * @param a the array to be filled.
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value.
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value.
     * @param val the value to be stored in all elements of the array.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *           <tt>toIndex > a.length</tt>
     */
    public static void fill(long[] a, int fromIndex, int toIndex, long val) {
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    }

    /**
     * Assigns the specified int value to each element of the specified array
     * of ints.
     *
     * @param a the array to be filled.
     * @param val the value to be stored in all elements of the array.
     */
    public static void fill(int[] a, int val) {
        fill(a, 0, a.length, val);
    }

    /**
     * Assigns the specified int value to each element of the specified
     * range of the specified array of ints.
     *
     * @param a the array to be filled.
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value.
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value.
     * @param val the value to be stored in all elements of the array.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *           <tt>toIndex > a.length</tt>
     */
    public static void fill(int[] a, int fromIndex, int toIndex, int val) {
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    }

    /**
     * Assigns the specified short value to each element of the specified array
     * of shorts.
     *
     * @param a the array to be filled.
     * @param val the value to be stored in all elements of the array.
     */
    public static void fill(short[] a, short val) {
        fill(a, 0, a.length, val);
    }

    /**
     * Assigns the specified short value to each element of the specified
     * range of the specified array of shorts.
     *
     * @param a the array to be filled.
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value.
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value.
     * @param val the value to be stored in all elements of the array.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *           <tt>toIndex > a.length</tt>
     */
    public static void fill(short[] a, int fromIndex, int toIndex, short val) {
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    }

    /**
     * Assigns the specified char value to each element of the specified array
     * of chars.
     *
     * @param a the array to be filled.
     * @param val the value to be stored in all elements of the array.
     */
    public static void fill(char[] a, char val) {
        fill(a, 0, a.length, val);
    }

    /**
     * Assigns the specified char value to each element of the specified
     * range of the specified array of chars.
     *
     * @param a the array to be filled.
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value.
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value.
     * @param val the value to be stored in all elements of the array.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *           <tt>toIndex > a.length</tt>
     */
    public static void fill(char[] a, int fromIndex, int toIndex, char val) {
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    }

    /**
     * Assigns the specified byte value to each element of the specified array
     * of bytes.
     *
     * @param a the array to be filled.
     * @param val the value to be stored in all elements of the array.
     */
    public static void fill(byte[] a, byte val) {
        fill(a, 0, a.length, val);
    }

    /**
     * Assigns the specified byte value to each element of the specified
     * range of the specified array of bytes.
     *
     * @param a the array to be filled.
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value.
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value.
     * @param val the value to be stored in all elements of the array.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *           <tt>toIndex > a.length</tt>
     */
    public static void fill(byte[] a, int fromIndex, int toIndex, byte val) {
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    }

    /**
     * Assigns the specified boolean value to each element of the specified
     * array of booleans.
     *
     * @param a the array to be filled.
     * @param val the value to be stored in all elements of the array.
     */
    public static void fill(boolean[] a, boolean val) {
        fill(a, 0, a.length, val);
    }

    /**
     * Assigns the specified boolean value to each element of the specified
     * range of the specified array of booleans.
     *
     * @param a the array to be filled.
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value.
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value.
     * @param val the value to be stored in all elements of the array.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *           <tt>toIndex > a.length</tt>
     */
    public static void fill(boolean[] a, int fromIndex, int toIndex,
                            boolean val) {
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    }

    /**
     * Assigns the specified double value to each element of the specified
     * array of doubles.
     *
     * @param a the array to be filled.
     * @param val the value to be stored in all elements of the array.
     */
    public static void fill(double[] a, double val) {
        fill(a, 0, a.length, val);
    }

    /**
     * Assigns the specified double value to each element of the specified
     * range of the specified array of doubles.
     *
     * @param a the array to be filled.
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value.
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value.
     * @param val the value to be stored in all elements of the array.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *           <tt>toIndex > a.length</tt>
     */
    public static void fill(double[] a, int fromIndex, int toIndex,double val){
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    }

    /**
     * Assigns the specified float value to each element of the specified array
     * of floats.
     *
     * @param a the array to be filled.
     * @param val the value to be stored in all elements of the array.
     */
    public static void fill(float[] a, float val) {
        fill(a, 0, a.length, val);
    }

    /**
     * Assigns the specified float value to each element of the specified
     * range of the specified array of floats.
     *
     * @param a the array to be filled.
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value.
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value.
     * @param val the value to be stored in all elements of the array.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *           <tt>toIndex > a.length</tt>
     */
    public static void fill(float[] a, int fromIndex, int toIndex, float val) {
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    }

    /**
     * Assigns the specified Object reference to each element of the specified
     * array of Objects.
     *
     * @param a the array to be filled.
     * @param val the value to be stored in all elements of the array.
     */
    public static void fill(Object[] a, Object val) {
        fill(a, 0, a.length, val);
    }

    /**
     * Assigns the specified Object reference to each element of the specified
     * range of the specified array of Objects.
     *
     * @param a the array to be filled.
     * @param fromIndex the index of the first element (inclusive) to be
     *        filled with the specified value.
     * @param toIndex the index of the last element (exclusive) to be
     *        filled with the specified value.
     * @param val the value to be stored in all elements of the array.
     * @throws IllegalArgumentException if <tt>fromIndex > toIndex</tt>
     * @throws ArrayIndexOutOfBoundsException if <tt>fromIndex < 0</tt> or
     *           <tt>toIndex > a.length</tt>
     */
    public static void fill(Object[] a, int fromIndex, int toIndex,Object val){
        rangeCheck(a.length, fromIndex, toIndex);
        for (int i=fromIndex; i<toIndex; i++)
            a[i] = val;
    }


    // Misc

    /**
     * Returns a fixed-size list backed by the specified array.  (Changes to
     * the returned list "write through" to the array.)  This method acts
     * as bridge between array-based and collection-based APIs, in
     * combination with <tt>Collection.toArray</tt>.  The returned list is
     * serializable.
     *
     * @param a the array by which the list will be backed.
     * @return a list view of the specified array.
     * @see Collection#toArray()
     */
    public static List asList(Object[] a) {
    return new ArrayList(a);
    }

    private static class ArrayList extends AbstractList
                       implements java.io.Serializable
    {
    private Object[] a;

    ArrayList(Object[] array) {
        a = array;
    }

    public int size() {
        return a.length;
    }

    public Object[] toArray() {
        return (Object[]) a.clone();
    }

    public Object get(int index) {
        return a[index];
    }

    public Object set(int index, Object element) {
        Object oldValue = a[index];
        a[index] = element;
        return oldValue;
    }
    }
}